We present a theoretical study of enhanced lateral and rotary photon drag within a four-level quantum-dot setup under the effect of dual interdot tunneling. Using the density-matrix formalism, we derive analytical expressions for the susceptibility, group index, and phase index under weak-field conditions. By introducing dual interdot tunneling in a four-level quantum-dot molecule, we demonstrate a mechanism for tunable, slowlight-enhanced photon drag, where the interaction between tunneling couplings and control fields allows precise manipulation of dispersion and light dragging. Our results reveal that rotary and lateral photon drag depend on the difference between the group and phase indices, leading to significant phase and frequency shifts even at relatively low translational and rotational velocities. The study highlights the potential of tunneling-coupled quantum-dot molecules as versatile platforms for slow-light-enhanced photon drag, with promising applications in precision metrology and nanoscale photonic devices.